1. X

    variation of parameter

    For this question, when we integrate x with d(y' + 3y)= e^(-4x) +4y with x , we got y' +3y= e^(-4x)/-4 + 4yx, we are unable to get f(x) , there is 4xy, ihow to solve this question??
  2. M

    Variation of Parameters work check

    Can someone check my work and see what I did wrong. This is an initial value problem. Here's the question and my answer: Here's my work. Sorry if it is hard to read.
  3. X

    variation of parameter

    in step2 , why thw y1 not equal to Acosx ? y2 not equal to Bsinx ? for second photo , why the author assume B+1 = B ?
  4. A

    Standard Deviation and Coefficient of Variation

    This is a sample problem for study purposes only: I have the solution to the Building A: but I am not sure how the numbers fit in the formula --I just need help understanding the concept and how it is used in this case in the most simple way possible. Also, Where did the ^5 come from? When I...
  5. V

    Trouble understanding method of variation of parameters

    Problem: y'''-3y''+4y = e^2x, solve using method of variation of parameters. Aux polynomial: r^3 -3r^2+4 = (r+1)(r-2)^2 therefore Y(homogeneous) = ae^-x + be^2x +cxe^2x. Now normally I would just take a guess at the particular solution and say its of the form: Ax^2e^2x. Then I would find...
  6. T

    variation of parameter to find second solution

    (1+t)^{3} \frac{d^{2}x}{dt^{2}}-(1+t)\frac{dx}{dt} + x = 0 i) show that x(t) = 1+t is a solution to this ODE ii) use variation of parameters to find another solution to this ode ie. write x(t) = c(t)(1+t) and fint c(t) I need help with part (ii) x(t) = (1+t) x'(t) = 1 x''(t)...
  7. R

    law of total probability - variation formal names?

    Hello, there are different variations of the law of total probability. For example, the probability of 3 discreet events all occurring is: A1 * A2 * A3 The probability of at least 1 of 3 discreet events occurring is: 1 - ((1 - A1) * (1 - A2) * (1 - A3)) Is there a formal name...
  8. J

    Good reference on multi-variable calculus of variation

    I am looking for a good and easy access reference on multi-variable calculus of variation with many examples and demonstrations. Although I have many books and references on the calculus of variation, most are focused on single-variable. Any advice will be appreciated.
  9. D

    What is the derivative of total variation?

    Let f(x) be a function of bounded variation on closed, bounded interval [a, b]. Let g(x) = V(f, [a, x]) where V(f, [a, x]) = \sum_{k=1}^n |f(x_{i}) - f(x_{i-1}) | given some partition P = \left \{a, x_{1}, x_{2}, ...., x_{n-1}, x \right \} of [a, x]. How can I calculate the derivate of...
  10. L

    function fo bounded variation!

    find P_{f}= [-1,2], N_{f}= [-1, 2] and T_{f}= [-1,2] if given that f(x)= |x|+1 for -1\leq x \leq 2 effort made; given that f(x)=|x|+1 for -1\leq x \leq 2 we have f(-1) = 2 f(2) = 3 so P_{f}[-1,2]= \sum_{j=1}^{2}[3-2]^{+} = [1]^{+} please help...
  11. D

    Variation on Recursive Bayesian Estimation

    Hi, I'm doing a research on a variation of Recursive Bayesian Estimation- it's a Bayesian estimation with a 'time smoothing' term: { \hat { P } }_{ k+1 }(x)\quad =\quad \eta \cfrac { { \hat { P } }_{ k }(x)p({ z }_{ k+1 }|x) }{ \int _{ -\infty }^{ \infty }{ { \hat { P } }_{ k }(x)p({ z }_{...
  12. A

    Joint variation

    Joint variation + percent The weight (W) that can be supported by a wooden beam varies directly as the square of its diameter (d) and inversely as its length (l). a) What percentage increase in the diameter would be necessary for a beam twice as long to support an equivalent weight? b)What...
  13. P

    Solving a DE by method of variation of parameters

    I have found the general solution for the equation of y'' - 9y = (x+1) e^{-x} to be y(x) = A e^{3x} + B e^{-3x} - \frac{1}{8} e^{-x} x - \frac{3 e^{-x}}{32} by the method of undetermined coefficients. However I need to use the method of variation of parameters, but I am totally confused. I...
  14. MoniMini


    "A varies directly with B when C is constant and inversely with C when B is constant. A=6, B=2 and C=3. What is the value of A when B = 3 and C= 18?" What I really don;t know here is how to form the equation/ statement. I've never really come acroos this question. Thanks :)
  15. V

    Variation of Binomial distribution

    The link to the problem.
  16. Ranger SVO

    Graduate Research (how much variation can I have?)

    I am currently working on a graduate research paper and statistics is not something I'm good at. In my proposal I need to compare the STAAR test scores of two schools. The demographics of the schools need to be representative of the average Texas school. African American 14%, Caucasian 35%...
  17. A

    Please help solving Linearly Dependent question for 4 variation

    cosx, sinx, ex, and e-x are LI or LD ( 0 =or< x =or< 1) I can see without calculation that it is LI but I do not know how to prove it. I tried to use Wronskian Determinant but it gets really messy W(x) = cosx sinx ex e-x -sinx cosx ex -ex -cosx -sinx ex e-x sinx -cosx ex e-x Someone...
  18. C

    Understanding total variation distance formula in relation to card shuffling.

    I am creating some JavaScript probability calculators related to magic the gathering deck building. While doing so I wondered what the best way to randomize a players deck is. I was able to find good information on 52 card decks stating that at-lest 7 riffle shuffle are needed according to...
  19. P

    variation of Euler Totient

    to calculate the number of integers co-prime to N and less than N we can simply calculate its ETF( Euler's totient function - Wikipedia, the free encyclopedia . )However to calculate the number of integers co-prime to N but less then X where X < N , how can we modify / calculate it ? I know how...
  20. B

    Need Some Help with Inverse and Direct Variation

    Hey guys haven’t been here in a while but have a few questions , I realize you all giving me the answers plainly wouldn’t really help me but if you could take me step by step into solving them if you can that would be help 1. Y varies directly as x and y is 2 when x is 3 calculate A) Y when X...